The move is designed to help Channel 4 diversify its revenue, with development currently at an early stage.
Luke Johnson, chairman of Channel 4, told the Sunday Telegraph: "There would be the potential for cross-marketing, promoting radio on TV as the BBC has done. We may even market the station through our sales arm."
Advertisers could be sold packages giving them airtime acroos television and radio.
It is believed that Channel 4 is holding discussions with United Business Media, which owns a national digital radio licence for a talk-based station.
This is currently used for the little-known Oneword station, but in a statement last week, UBM said that it expected to announce details of a new partner for Oneword in the next few months.
The Channel 4 radio project is being funded by a £90m pot set aside for new ventures. Plans for the station are being developed by Johnson along with Rob Woodward, commercial director of Channel 4's commercial arm, 4 Ventures. Kevin Lygo, director of television programming, is also reported to be closely involved.
Channel 4 is owned by the government, although there have been reports that it could look at selling off the broadcaster, which would allow Channel 4 to merge with rival Five. The two have held talks and Channel 4 executives are understood to have lobbied the government on a change of ownership.
Last month, Channel 4 appointed Andy Duncan as its new chief executive, after Mark Thompson was appointed to the role of director-general at the BBC.
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